Two people are holding an object ... one says all of it is his and the other says half of it is his. The first swears that no less than three quarters are due him, and the second swears that no less than one quarter is due him. The first receives three quarters and the second receives one quarter.
Talmud, Baba Metzia
Abstract
One of the few “laws” of political science is the fairly regular relationship in any given plurality electoral system known as thecube law, transforming vote shares into seat shares. In this paper, we develop an altogether different and more robust paradigm relating seats to votes which generates similar results as the cube law. In our model, political parties bargain with each other for an expected number of seats using the ability to gerrymander in determining their bargaining strength. We find that an arbitrated solution to the seat-vote allocation problem generates solutions remarkably similar to the conventional cube-law-based solutions. Thus our model can in some way replace the cube law paradigm. With our model, we are able to evaluate the impact ofBaker v. Carr (1962) on gerrymandering. We also find that proportional representation results can be achieved within our model by allowing non-zero population deviations between districts.
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I am grateful for the comments and criticism of David Levy, Bernard Grofman, Charles Rowley, William Crain, and Robert Tollison. Responsibility for all errors, of course, remains mine alone. This paper does not necessarily reflect the views of the American Association of Retired Persons.
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Cohen, L.M. The bargaining range in legislative district apportionment. Public Choice 77, 467–491 (1993). https://doi.org/10.1007/BF01047856
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DOI: https://doi.org/10.1007/BF01047856